Trans-Planckian Effects in Inflationary Cosmology and the Modified Uncertainty Principle

There are good indications that fundamental physics gives rise to a modified spacemomentum uncertainty relation that implies the existence of a minimum length scale. We implement this idea in the free scalar field theory that describes density perturbations in flat Robertson-Walker space-time. This leads to a non-linear timedependent dispersion relation that encodes the effects of Planck scale physics in the inflationary epoch. Unbounded dispersion relations are excluded by the minimum length principle. We also find red-shift induced modifications of the field theory that tend to dampen the fluctuations at trans-Planckian momenta. In the specific example considered, this feature helps determine the initial state of the fluctuations, leading to a flat power spectrum.